Mathematics-Online lexicon: Surface Integrals of Scalar Functions

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	Mathematics-Online lexicon:
	Surface Integrals of Scalar Functions

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Let

be a surface with regular parametrization $\sigma: A \longrightarrow \mathbb{R}^3 \ ,\ (t,u) \mapsto \sigma(t,u) .$ Further let

be a differentiable scalar function defined on an open set containing

Then the integral

$\displaystyle \iint\limits_S f \ d\sigma := \iint\limits_A f(\sigma(t,u)) \vert\sigma_t \times \sigma_u \vert \ dt du$

is called the surface integral of over The value of the integral does not depend on the parametrization.

If represents a density of mass then the integral yields the mass of the surface.

If then the integral just gives the area of the surface.

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automatically generated 7/ 5/2005